6. Solve the following recurrence relations: (a) An+1 ,00 = 2 (b) n-1 an+1 =1+ ak...
6. Solve the following recurrence relations: (a) An+1 = 2 an , AO = 2 (b) n-1 An+1 =1+ ak , 0o = a1 = 1 ,n> 1 k=0
Solve the following recurrence relations: (a) an+1 = a ,20 = 2 (b) n-1 An+1 = 1+ ak ,20 = a1 = 1 ,n> 1 k=0
Solve the following recurrence relations and give the value of f(N) f(n) = -1 for n= 0 f(n) = f(n-1)+ n for n>0
1) Use Generating Functions to solve each of the following recurrence relations: (a) a(n)=2a(n-1)-a(n-2) if n>1, while a(0)=2, a(1)=1
For these recurrence relations, solve for general equation using characteristics and particular. Use initial condition if given. a. fn+1 = 1 Initial condition: fo = 2 b. fn+1 -fn-n=0 n-1 1+fi = fn+1 Initial conditions: fo = 1, f1 = 1, n > 1 i=0
2.5. Solve the following recurrence relations and give a Θ bound for each of them. (e) T(n) 8T(n/2) n (f) T(n) = 49T(n/25) + n3/2 log n (g) T(n) = T(n-1) + 2 (h) T(n) T(n 1)ne, where c 21 is a constant (i) T(n) = T(n-1) + c", where c > 1 is some constant (j) T(n) = 2T(n-1) + 1 (k) T(n) T(vn) +1
Solve the recurrence relation: a subn = 5a subn-1 - 6 a subn-2 n is greater than or equal to 2 given: ao = 1, a1 = 0
Solve the recurrence relations: T(n) = 4T(n/2)+1 when n>2 and T(n) = 1 when n = 2. T(n) = 4T(n/4)+1 when n>4 and T(n) = 1 when n = 4
2) [PI 1.2||PI 1.3]Use characteristic equation to solve the recurrence relation. ak= - 10ak-1 - 25ak-2, 20 = 1; a1 = -1 use the equation an= rom +2 nrm for repeated roots. ( 20 Points)
8. Consider the following simultaneous homogeneous recurrence relations: 3a-12bn-1 bn-an-1 + 2bn-1 for n > 1, with initial conditions ao 1 and bo - 0 (a) Find the generating function for an and then solve for an b) What is the homogeneous recurrence relation that an satisfies? (c) Repeat (a) and (b) for bn 72. 8. Consider the following simultaneous homogeneous recurrence relations: 3a-12bn-1 bn-an-1 + 2bn-1 for n > 1, with initial conditions ao 1 and bo - 0...